SOPMOD doesn't denote a particular barrel length (Special Operations Peculiar MODification) it refers to a specific group of attachments or modifications. I assumed that you meant a traditional M4A1 length when you said SOPMOD. There are many different lengths of barrel for AR's the ones I listed are the most common sizes.

If price isn't a factor then I would put the same barrel and hot-up/rubber/nub in a 20" barrel as I would a 12.5" barrel. This will provide virtually the same performance from each barrel.

Prometheus EG barrel
ProWin V2 hop-up unit
Purple Prometheus hop-rubber
Firefly Flat hop-nub
The rubber will need to be flat hopped. (remove any protrusions from the inside of the rubber) Fairly common modification, plenty of tutorials available on the internet.
Some may tell you to do an Rhop but it requires much more skill and labour to do it properly, not generally recommended for the novice.

Inside your gearbox is going to depend greatly on what you're after, Rate of fire, trigger response, if you're already satisfied with those things, no need to change anything. Make sure you have good air seal inside and between your mechbox and your hop unit. Good air seal is key to consistency/accuracy in AEG's.